Question 1084659
the area of the deck is 50 square feet.


the area is represented by x^2 + 5x


your equation becomes x^2 + 5x = 50


subtract 50 from both sides of this equation to get x^2 + 5x - 50 = 0


factor this quadratic equation to get (x+10) * (x-5) = 0


your questions are:


Step 1: x^2+5x=50


correct.


Step 2: x(x+5)=50 The length is x. What is the width? ___


if the length is x, then the width has to be x + 5.


Step 3: x^2 + 5x - 50 = 0


correct.


Step 4: (x+10)(x-5)=0 


correct.


Because the length can't be ___, the length is 5, and the width is ___.


your factors are (x+10) * (x-5) = 0


to make this equation true, either x+10 is equal to 0 or (x-5) is equal to 0, or both.


set each factor equal to 0 and solve for x.


with x + 10 = 0, solve for x to get x = -10


with x - 5 = 0, solve for x to get x = 5


the length of the rectangle has to be positive, so x can't be equal to -10, therefore x = 5.


x is equal to 5 which represents the length.


x+5 is equal to 10 which represents the width.


length * width = 5 * 10 which is equal to 50 square feet.